[Paper Review] Exploiting Newton-factorized, 2PN-accurate, waveform multipoles in effective-one-body models for spin-aligned noncircularized binaries

A. Placidi, Simone Albanesi+4 more|arXiv (Cornell University)|Dec 10, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy61 references41 citations

TL;DR

This paper introduces a novel Newton-factorized, 2PN-accurate waveform multipole factorization for effective-one-body (EOB) models in spin-aligned, noncircular binary systems. By separately resumming the circular part via standard EOB methods and the noncircular 2PN residual—especially the tail contribution—using Padé approximants, the model achieves sub-0.05 rad phase accuracy at pericenter for eccentricities up to e = 0.9, significantly improving over Newtonian-only factorization.

ABSTRACT

We present a new approach to factorize and resum the post-Newtonian (PN) waveform for generic equatorial motion to be used within effective-one-body (EOB) based waveform models. The new multipolar waveform factorization improves previous prescriptions in that: (i) the generic Newtonian contribution is factored out from each multipole; (ii) the circular part is factored out and resummed using standard EOB methods and (iii) the residual, 2PN-accurate, noncircular part, and in particular the tail contribution, is additionally resummed using Pad\'e approximants. The resulting waveform is validated in the extreme-mass-ratio limit by comparisons with nine (mostly nonspinning) numerical waveforms either from eccentric inspirals, with eccentricities up to $e=0.9$, or dynamical captures . The resummation of the noncircular tail contribution is found essential to obtain excellent (${\lesssim}0.05$~rad at periastron for $e=0.9$) analytical/numerical agreement and to considerably improve the prescription with just the Newtonian prefactor. In the comparable mass case, the new 2PN waveform shows only a marginal improvement over the previous Newtonian factorization, though yielding maximal unfaithfulness $\simeq 10^{-3}$ with the 28 publicly available numerical relativity simulations with eccentricity up to $\sim 0.3$ (except for a single outlier that grazes $10^{-2}$). We finally use test-particle data to validate the waveform factorization proposed by Khalil et al.~[Phys.~Rev.~104 (2021) 2, 024046] and conclude that its amplitude can be considered reliable (though less accurate, $\sim 6\%$ fractional difference versus $1.5\%$ of our method) only up to eccentricities $\sim 0.3$.

Motivation & Objective

• To improve analytical waveform models for eccentric, spin-aligned binary black hole systems by incorporating higher-order post-Newtonian (PN) corrections.
• To address the lack of 2PN-accurate, noncircular waveform information in existing EOB models like TEOBResumS.
• To validate the new factorization scheme against numerical relativity waveforms in both extreme-mass-ratio and comparable-mass regimes.
• To assess the reliability of alternative factorization schemes, such as the one proposed by Khalil et al. [Phys. Rev. 104, 024046 (2021)].

Proposed method

• Factorizing each EOB multipole using a generic Newtonian prefactor derived from time-derivatives of Newtonian mass and current multipoles.
• Separately resumming the quasi-circular part using standard EOB resummation techniques.
• Extracting the 2PN-accurate noncircular residual, particularly the tail contribution, by subtracting both Newtonian and circular parts.
• Applying Padé approximants to resum the noncircular 2PN residual for improved convergence and accuracy.
• Validating the model against 9 numerical relativity waveforms from eccentric inspirals (e ≤ 0.9) and dynamical captures in the test-particle limit.
• Performing direct phasing comparisons with 28 public NR simulations for comparable-mass binaries (e ≤ 0.3).

Experimental results

Research questions

• RQ1 Can a Newton-factorized, 2PN-accurate, and Padé-resummed EOB waveform model achieve sub-0.05 rad phase accuracy at pericenter for highly eccentric binaries (e ≈ 0.9)?
• RQ2 How does the inclusion of 2PN noncircular corrections, especially the tail contribution, improve agreement with numerical relativity compared to Newtonian-only factorization?
• RQ3 What is the performance of the new EOB model in the comparable-mass regime with moderate eccentricities (e ≤ 0.3)?
• RQ4 How does the proposed factorization compare in accuracy to the alternative scheme by Khalil et al. [Phys. Rev. 104, 024046 (2021)] for eccentric systems?
• RQ5 Is the resummation of the noncircular tail contribution essential for high-accuracy modeling in the extreme-mass-ratio limit?

Key findings

• The resummation of the noncircular 2PN tail contribution is essential to achieve phase agreement within ≲0.05 rad at pericenter for e = 0.9, significantly outperforming Newtonian-only factorization.
• In the extreme-mass-ratio limit, the new model achieves excellent agreement with numerical waveforms from eccentric inspirals (e ≤ 0.9) and dynamical captures, validating the 2PN and Padé resummation approach.
• For comparable-mass binaries with eccentricities up to ∼0.3, the new 2PN waveform yields maximal unfaithfulness ≃10−3 compared to 28 public NR simulations, with one outlier reaching ∼10−2.
• The alternative factorization scheme by Khalil et al. is found to be reliable only up to eccentricities ∼0.3, with a fractional amplitude difference of ∼6% compared to the new method’s ∼1.5%.
• The improvement from Newtonian to 2PN factorization is marginal in the comparable-mass case, indicating that the dominant error source lies beyond 2PN or in other model components.
• The study confirms that the 2PN-accurate, Newton-factorized, and Padé-resummed waveform model is a robust and accurate extension of TEOBResumS for noncircular, spin-aligned binaries.